Question 4(vii)
Simplify :
$(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$

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Solution

$(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2} = (m^{2})^{2} - 2 \times m^{2} \times n^{2} m + (n^{2} m)^{2} + 2 m^{3} n^{2}$
$[U s i n g i d e n t i t y (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
$m^{4} - 2 m^{3} n^{2} + n^{4} m^{2} + 2 m^{3} n^{2}$
$= m^{4} + n^{4} m^{2}$

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(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}

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